Question

Sabendo que (x+1/x)^2=12,determine 1/x^2+x^2

Answer 1

Resposta:

$\boxed{\mathsf{10}}$

Explicação passo-a-passo:

$\\ \displaystyle \mathsf{\left ( x + \frac{1}{x} \right )^2 = 12} \\\\\\ \mathsf{x^2 + 2 \cdot x \cdot \frac{1}{x} + \frac{1}{x^2} = 12} \\\\\\ \mathsf{x^2 + 2 + \frac{1}{x^2} = 12} \\\\\\ \mathsf{x^2 + \frac{1}{x^2} = 12 - 2} \\\\\\ \boxed{\boxed{\mathsf{x + \frac{1}{x^2} = 10}}}$

Answer 2

Resposta:

Explicação passo-a-passo:

( x + 1/x)² = 12

[ (x)²  +  2 * x *  1/x   +  (1/x)²  ] = 12

[ x² + 2x/x +  1/x² = 12 ]

cortando x de 2x/x

{ x²  + 2  +  1/x²  = 12

x² + 1/x²  = 12 - 2

x² + 1/x² = 10 *** ou   1/x²  + x²  = 10